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the POLAR and DMSP spacecraft in the high-latitude
magnetosphere
T. J. Stubbs, M. Lockwood, P. Cargill, M. Grande, B. Kellett, C. Perry
To cite this version:
T. J. Stubbs, M. Lockwood, P. Cargill, M. Grande, B. Kellett, et al.. A comparison between ion
characteristics observed by the POLAR and DMSP spacecraft in the high-latitude magnetosphere.
Annales Geophysicae, European Geosciences Union, 2004, 22 (3), pp.1033-1046. �hal-00317281�
SRef-ID: 1432-0576/ag/2004-22-1033 © European Geosciences Union 2004
Annales
Geophysicae
A comparison between ion characteristics observed by the POLAR
and DMSP spacecraft in the high-latitude magnetosphere
T. J. Stubbs1,2, M. Lockwood3, P. Cargill1, M. Grande3, B. Kellett3, and C. Perry3 1Space & Atmospheric Physics, The Blackett Laboratory, Imperial College London, UK
2Laboratory for Extraterrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA 3Space Science Department, Rutherford Appleton Laboratory, Oxfordshire, UK
Received: 31 October 2002 – Revised: 12 August 2003 – Accepted: 5 September 2003 – Published: 19 March 2004
Abstract. We study here the injection and transport of ions
in the convection-dominated region of the Earth’s magneto-sphere. The total ion counts from the CAMMICE MICS in-strument aboard the POLAR spacecraft are used to generate occurrence probability distributions of magnetospheric ion populations. MICS ion spectra are characterised by both the peak in the differential energy flux, and the average energy of ions striking the detector. The former permits a compar-ison with the Stubbs et al. (2001) survey of He2+ ions of solar wind origin within the magnetosphere. The latter can address the occurrences of various classifications of precip-itating particle fluxes observed in the topside ionosphere by DMSP satellites (Newell and Meng, 1992). The peak energy occurrences are consistent with our earlier work, including the dawn-dusk asymmetry with enhanced occurrences on the dawn flank at low energies, switching to the dusk flank at higher energies. The differences in the ion energies observed in these two studies can be explained by drift orbit effects and acceleration processes at the magnetopause, and in the tail current sheet. Near noon at average ion energies of ≈1 keV, the cusp and open LLBL occur further poleward here than in the Newell and Meng survey, probably due to convection-related time-of-flight effects. An important new result is that the pre-noon bias previously observed in the LLBL is most likely due to the component of this population on closed field lines, formed largely by low energy ions drifting earthward from the tail. There is no evidence here of mass and mo-mentum transfer from the solar wind to the LLBL by non-reconnection coupling. At higher energies (≈2–20 keV), we observe ions mapping to the auroral oval and can distinguish between the boundary and central plasma sheets. We show that ions at these energies relate to a transition from dawn-ward to duskdawn-ward dominated flow, this is evidence of how ion drift orbits in the tail influence the location and behaviour of the plasma populations in the magnetosphere.
Correspondence to: T. J. Stubbs
(tstubbs@lepvax.gsfc.nasa.gov)
Key words. Magnetospheric physics (magnetopause, cusp
and boundary layers; magnetosphere-ionosphere interac-tions; magnetospheric configuration and dynamic)
1 Introduction
In order to understand how mass and energy flow into and around the magnetosphere, we must be able to relate plasma populations observed at different locations. This, in turn, re-quires us to understand the transport mechanisms involved. The coupling between the solar wind/magnetosheath and magnetosphere is driven by magnetic reconnection at the dayside magnetopause, which creates open field lines that allow plasma to cross this boundary. On crossing the magne-topause, magnetosheath plasma is accelerated and then dis-persed by convection as it precipitates into the high-latitude dayside magnetosphere creating the open and low-latitude boundary layer (LLBL), as well as the cusp and mantle re-gions. It has been proposed that other injection mechanisms or re-closure of open field lines by lobe reconnection could produce an LLBL on closed field lines (see review by Lock-wood, 1997). The plasma component remaining on these field lines until they are closed by magnetic reconnection in the tail is trapped within the magnetosphere and subsequently accelerated earthward. The velocity of the particles in this component of the plasma increases by the Alfv´en speed with each crossing of the midtail current sheet (see Onsager and Mukai, 1995 and references therein). The charged particles in this plasma then follow drift orbits which depend on the convection electric field and the particle charge and energy. Thus, the observed distribution of these particles depends on the above three factors.
A study of the distribution of ions of solar wind ori-gin within the magnetosphere was undertaken by Stubbs et al. (2001) (hereafter referred to as Stubbs et al.), using He2+ ions detected by the CAMMICE MICS instrument aboard
POLAR as a tracer. In this study each integration period was characterised by the energy at the peak in the differen-tial energy flux (JE) spectrum between ≈1 and 200 keV.e−1
(hereafter referred to as “the peak energy”), and the occur-rence probabilities were plotted as a function of invariant latitude (3) and magnetic local time (MLT). In the energy range from 1.8 to 21.4 keV an enhancement was observed along the dawn flank between 3≈68◦ and 75◦, giving rise to a dawn-dusk asymmetry. This asymmetry was shown not to be caused by direct entry of particles into the mag-netosphere (i.e. neither the Svalgaard-Mansurov effect nor a dawn-dusk asymmetry in Fermi acceleration at a quasi-parallel bow shock), but by ions drifting earthward from the tail, as was demonstrated by sorting the data by energy and the sense of the interplanetary magnetic field Z−component (IMF BZ). The asymmetry was shown to change to the dusk
flank at higher energies, with the energy at which the peak in the occurrence flips from the dawn to the dusk flank (here-after referred to as the “cross-over” energy) being estimated at ≈23 keV. This flip in the asymmetry occurred at slightly lower energies for northward IMF conditions due to the con-vection electric field being weaker at these times, a behaviour consistent with that of ions executing drift orbits (Lyons and Williams, 1984b). The cusp was isolated in this study at en-ergies between 1.8 and 6.9 keV.
The precipitation into the dayside ionosphere at low alti-tudes was classified and mapped by Newell and Meng (1992) (hereafter referred to as Newell and Meng) from observa-tions made by the SSJ/4 spectrometers aboard the Defense Meteorological Satellite Program (DMSP) spacecraft. They used an automated identification scheme to produce occur-rence frequency maps for observing various types of plasma precipitating into the ionosphere. The classifications and re-sults from this survey are discussed in more detail in Sect. 4. The fleet of DMSP spacecraft are in Sun synchronous po-lar orbits at an altitude of around 830 km. The SSJ/4 instru-ments are particle spectrometers which measure precipitating electron and ion fluxes between 30 eV and 30 keV every sec-ond (Hardy et al., 1984). The look direction is within a few degrees of the local vertical, in order to detect precipitating particles with pitch angles inside the loss cone. Stubbs et al. carried out a brief comparison between their He2+ion occur-rences and the Newell and Meng survey and showed them to be qualitatively consistent.
More recently, Friedel et al. (2001) studied the access of plasma sheet particles into the inner magnetosphere using data from the Hydra hot plasma experiment (Scudder et al., 1995) aboard POLAR. Using a formulation introduced by Whipple (1978), they showed that, in general, the occur-rence distributions of ions and electrons were globally con-sistent with the conventional drift paradigm; thus, validating the simple corotation and convection electric fields used in their analysis. They were also able to describe the average particle transport over a wide range of geomagnetic activ-ity levels. This result was based mainly on the electron data which was very well ordered by the Alfv´en boundaries (see Wolf, 1995). The ion data, however, was not that well
or-ganised, probably due in part to the more complex ion drift orbits.
There is an overlap in the range of energy detection of the SSJ/4 spectrometers and MICS from ≈1 to 30 keV. In or-der to compare our results with the Newell and Meng sur-vey, and other instruments that measure total ion flux, such as POLAR/Hydra, we survey the total ion signature at PO-LAR using data from the MICS DCR (Double Coincidence Rate) channel. In characterising the different types of parti-cle precipitation, Newell and Meng use the average energy of ion precipitation striking the atmosphere as a criterion to dis-tinguish between precipitation types. Therefore, we survey the total ion flux at POLAR, using both the peak and average ion energies as a bridge between the Stubbs et al. survey and the work of Newell and Meng. Our aim is to understand how the ion injection and transport processes invoked to explain the observations of Stubbs et al. and Friedel et al. (2001) relate to the precipitating particle occurrence frequency dis-tributions observed in the ionosphere by Newell and Meng. In Sect. 2 we give a brief description of the POLAR space-craft and the CAMMICE MICS instrument used in this study. Sect. 3 gives details of the data processing and presentation used in this work, and includes a discussion of particle fluxes and coordinate systems. The various dayside particle pre-cipitation characteristics used by Newell and Meng are de-scribed in Sect. 4, and are important for relating their results with those presented in this paper. Sect. 5 contains the results and interpretation: Sect. 5.1 concentrates on the peak ion en-ergy results and the comparison with the work of Stubbs et al.; Sect. 5.2 discusses the average ion energy results and fo-cuses more on the comparison with the Newell and Meng survey. Finally, in Sect. 6, we present the discussion and conclusions.
2 Spacecraft and instrumentation
The POLAR spacecraft is in a 1.8×9 RE polar orbit with an
inclination of ≈86◦to the equator and a period of ≈17.5 h (Acu˜na et al., 1995). Its apogee is at high northern lati-tudes and is spin-stabilised at 10 rpm, with its spin axis ap-proximately perpendicular to the orbital plane. The data set used in this study is from the Magnetospheric Ion Composi-tion Sensor (MICS) of the Charge and Mass Magnetospheric Ion Composition Experiment (CAMMICE). The Electro-static Analyser (ESA) on MICS sorts by energy per charge (E/q) and has 32 steps (0–31), with E/q mid-points ranging from 1.0–416.7 keV.e−1. The ESA has an energy resolution
1E/E ≈16% full width at half maximum, so the E/q range of the detector is effectively from 0.9 to 450.0 keV.e−1. For most of the mission, only steps 0–24 have been used, re-ducing the effective E/q range to 0.9–208.8 keV.e−1. Sort-ing by the ESA, combined with time-of-flight measurements and determination of the energy deposited in the solid state detector, allows the MICS to determine the flux, mass and charge states of the incident ions (Wilken et al., 1992; Fritz et al., 1997). MICS has a temporal resolution of 197.5 s; it
takes data at one ESA step per rotation (6 s), thereby requir-ing 192 s to make an observation at every ESA step, plus 5.5 s to reset for the next set of measurements. Raw count rates (counts.s−1) are calculated by averaging over the spacecraft spin period (6 s).
3 Data processing and presentation
We survey the DCR ion energies in the E/q mid-point range of 1.0–23.3 keV.e−1. The DCR counts are dominated by pro-tons with a charge state of +1, for which this is equivalent to an energy range of 1.0–23.3 keV. For studies of the peak energy this gives an effective energy range of 0.9–25.2 keV due to the spread of energies about the channel midpoints given by the energy resolution. As was done in Stubbs et al., we search for the peak in the JE spectra over the whole
en-ergy range (≈1–200 keV.e−1). To calculate the average ion energy we use ESA channels from 0 to 12, corresponding to midpoints from 1.0 to 30.9 keV.e−1; this is done to achieve the best possible comparison with average ion energies de-termined from the SSJ/4 instruments aboard DMSP. For the average energy studies we bin the data using the same energy midpoints as the E/q channels. However, the average energy for each bin extends to the midpoint between each E/q chan-nel, this is calculated using logarithmic interpolation. There-fore, the average ion energies in the survey range from 0.9 to 26.83 keV.
To avoid using single counts, which can be created by anomalous events in the detectors, we set the minimum raw count rate at 1 count.s−1, so 6 counts in an integration period are required for it to register ions as present. A maximum raw count rate of 2500 counts.s−1 was also set, as cosmic
rays striking a detector can lead to anomalously high count rates (≈10 000 counts.s−1in the DCR channel).
We calculate the average energy, <E>, from the ratio of the integral energy flux (FE) to the integral number flux (F ):
< E >=FE F = U P i=L JEi U P i=L Ji = U P i=L CCi U P i=L CCi Ei . (1)
In the above equation: JEi and Ji are the differential
en-ergy and differential number fluxes per channel, respectively;
Land U represent the lower and upper ESA steps, respec-tively, in this case L=0 and U =12 (energy midpoint of 30.9 keV.e−1); C
Ci and Ei are the corrected count rate and
energy detected at each channel, respectively. (CC is
deter-mined by dividing the raw count rate by the channel effi-ciency.) As the geometric factor is the same for all MICS channels, it can be removed from the differential flux per channel terms and cancelled in Eq. (1); thus, leaving just the CCi and Ei terms in the equation (for a more detailed
discussion of particle instrument fluxes, see Stubbs, 2002). This eliminates the need for absolute fluxes, as is the case for determining the peak energy.
The method for calculating average ion energy shown in Eq. (1) is used by the Air Force Research Laboratory (AFRL) when analysing DMSP SSJ/4 particle data (Newell, personal communication). This definition of <E> corresponds to the average energy of particle precipitation striking the at-mosphere or the detector. (This does not correspond to the average energy moment of the distribution function.) The
<E>value given by Eq. (1) is weighted toward the higher energy particles, as more of the higher energy faster moving particles strike the detector/atmosphere per unit time than the slower low energy particles. As a result, it has a higher value than the average energy given by the moment of the distribu-tion funcdistribu-tion, which considers the average energy of particles in a given volume of phase space.
In order to facilitate a direct comparison with Stubbs et al., we plot the occurrence probability of observing ions based on the peak energy selection criteria as a function of invari-ant latitude (3) and magnetic local time (MLT), as shown in Fig. 2. We calculate invariant latitude using the McIlwain L parameter, also referred to as Lm or L-shell (McIlwain,
1966). This is calculated using the SHELLIG routines (avail-able from NSSDC FTP site), which uses the IGRF magnetic field model. As we are interested in particles on drift orbits, where the magnetic moment and the second adiabatic invari-ant are generally conserved, these coordinates should order the data well.
The occurrences based on the average energy selection cri-teria, shown in Fig. 3, are plotted as a function of Corrected Geomagnetic (CGM) latitude and MLT. The CGM coordi-nates, as described by Baker and Wing (1989), were used by Newell and Meng to order their data. (CGM latitude is later referred to as MLAT, to be consistent with the nomenclature used by Newell and Meng.) As the code for calculating CGM coordinates (available from the JHU/APL website) is based on the IGRF model and limited to altitudes below 40 000 km, we traced field lines from POLAR to the Earth’s surface us-ing the T01 model (Tsyganenko, (2002a, b) before convert-ing into CGM coordinates. T01 is an empirical model that has been generated using a large database of magnetic field observations. This has included data from the Magnetic Field Experiment (MFE) aboard POLAR, which has improved the modelling of the dayside Birkeland current systems. As near field-aligned particles tend to follow magnetic field lines, this should relate our study well to the occurrence frequencies of Newell and Meng. Assuming that there are no system-atic errors in the T01 field line mapping, we would expect differences to be due to energy and pitch angle dependent dispersion caused by the convection of field lines during the time-of-flight from the reconnection X-line to POLAR and DMSP altitudes. The T01 model is dependent on the solar wind dynamic pressure, IMF BY and BZ, and the Dst index,
as well as time and location. These solar wind parameters were obtained from the Magnetic Field Investigation (MFI) and Solar Wind Experiment (SWE) aboard the WIND space-craft. The MFI and SWE datasets were validated, joined and time lagged to the Earth, using the techniques described in Stubbs et al. (2003).
Fig. 1. A map of the ionosphere to the magnetosphere based on plasma characteristics as a function of MLAT and MLT (adapted from Newell and Meng, 1992). Data was taken for all interplanetary conditions (© by American Geophysical Union).
The MLT in both cases is calculated using the method de-scribed by Baker and Wing (1989), which takes into account effects due to seasonal changes and the eccentricity of the Earth’s orbit. Though, of course, it is calculated using the magnetic longitude at the spacecraft for the peak ion survey (Fig. 2) and the CGM longitude at the T01 footpoint for the average ion energy survey (Fig. 3).
The differences between 3 and MLAT (calculated in the manner described above) are most noticeable at high-latitudes, where 3 tends to place observations further pole-ward than MLAT. This is because, unlike the T01 model, the near-dipolar IGRF model used in determining 3 takes no ac-count of the distortion of the magnetospheric field from ex-ternal currents. This distortion is primarily due to the com-pression of the magnetosphere, particularly at the dayside magnetopause. This means that magnetospheric field lines are moved poleward relative to the more dipolar IGRF field lines, hence, the discrepancy between 3 and MLAT. Also, when calculating MLAT we follow a magnetic field line to the Earth’s surface along a magnetic shell; whereas in calcu-lating 3 we trace along an L-shell where adiabatic invariants are conserved. This also leads to a further discrepancy be-tween 3 and MLAT; however, compared to the differences due to external currents this is negligible.
The occurrence plots in Figs. 2 and 3 cover latitudes from 60◦to 90◦at all MLTs in 1.5◦by 24 min bins. (The survey was also carried out for smaller bins of 0.5◦ width in lati-tude and all the features reported here were evident, with the addition of a slightly increased statistical fluctuation level
be-cause sample numbers in each bin were lower.) The occur-rence probability was calculated by dividing the number of times POLAR observed ions by the total number of samples made in that bin. Plotting occurrence probabilities removes any biasing in the data caused by the orbit or instrument sam-pling. To ensure all bins are statistically significant, we have removed any bins sampled less than 50 times. This means an anomalous event will only register a 2% probability at most. The occurrence probability scale bar was standardised from 0 to 70% in the plots, to allow for a direct comparison. The data coverage in this study has been extended from that used in Stubbs et al. to be almost continuous from 18 March 1996 to 31 March 2000.
An important consideration when comparing data from the DMSP SSJ/4 instruments and MICS is that the SSJ/4 observe only precipitating ions in the loss cone which would have been near field-aligned at the greater altitude of the POLAR satellite, whereas MICS observes both precipitating magne-tospheric and outflowing ionospheric ion populations at a range of pitch angles. One such source of ionospheric plasma is the polar wind. In the region of the cusp, the cleft ion foun-tain also populates the magnetosphere with O+and H+ions, particularly during active times (Shelley, 1986; Lockwood et al., 1985; Hultqvist et al., 1988). Ionospheric outflow has been observed in the auroral regions in the form of ion beams and conics with energies of 0.1 to 10 keV (e.g. Mizera and Fennell, 1977; Ghielmetti et al., 1978). This could possibly lead to significant discrepancies between our survey and that of Newell and Meng.
Fig. 2. The occurrence probability of ions in the magnetosphere plotted as invariant latitude (3) versus magnetic local time (MLT) in polar coordinates. Occurrence probabilities for energy ranges: (a) 0.9–1.1 keV, (b) 1.2–2.6 keV, (c) 2.9–8.0 keV and (d) 9.1–25.2 keV. The peak in the DCR (total ion signature) differential energy flux spectrum (JE) is used to determine a characteristic energy for each integration period.
3ranges from 60◦to 90◦for all MLTs with a bin size of 1.5◦by 24 min. Each bin has a 50-sample threshold to ensure reliable statistics. Data has been taken for all interplanetary conditions. CAMMICE data used in this plot was taken almost continuously from 18 March 1996 to 31 March 2000.
4 The dayside particle precipitation classifications used by Newell and Meng
The identification of the various types of particle precipita-tion by Newell and Meng was done using a neural network technique described by Newell et al. (1991b). This technique was adopted by these authors as it can be difficult to distin-guish quantitatively between different types of precipitation, although conceptually there is often a clear distinction.
In Table 1 we list the particle precipitation classifications that are most relevant to our study, with typical average ion energy values and integral fluxes based on descriptions and examples given in Newell et al. (1991b, c). It is important to note that the classification of particle precipitation sum-marised here is based on both electron and ion spectra; there-fore regions with similar ion characteristics (e.g. void and polar rain) are distinguished by their electron spectra. The schematic in Fig. 1 shows a map of ionospheric precipitation based on the results from Newell and Meng. It is impor-tant to note that in the following discussions we compare our
results with the original Newell and Meng occurrence fre-quency plots shown in their Fig. 1, and not the schematic shown in their Fig. 2 (and reproduced here in Fig. 1). In their survey, the absence of any significant precipitation is termed void (≈0.01 ergs.cm−2.s−1). Polar rain is typically
observed as low energy electron precipitation in the polar cap often during southward IMF, as identified by Winning-ham and Heikkila (1974). Mantle is classed as a region of low energy ion precipitation poleward of the dayside auroral oval, as described by Newell et al. (1991a). Cusp refers to magnetosheath plasma that has gained direct entry into the magnetosphere. Cusp ions are characterised as having low temperature with high bulk flow velocity; this is described at length in Newell and Meng (1988, 1990). Plasma in the low latitude boundary layer (LLBL) is described as “varying considerably”, but generally exhibits higher thermal temper-atures and lower bulk flow than in the magnetosheath, and contains high energy particles of magnetospheric origin near the magnetopause, as described by Eastman et al. (1985) and Sckopke et al. (1981).
Fig. 3. The occurrence probability of average ion energies: (a) 0.9–1.53 keV, (b) 1.53–2.10 keV, (c) 2.10–4.85 keV, (d) 4.85–8.55 keV, (e) 8.55–15.20 keV and (f) 15.20–26.83 keV. In each integration period, the average energy of ions between 0.9 and 30.9 keVe detected by the DCR channel is determined. (Average ion energy <E>=FE/F.) These occurrences are plotted as a function of MLAT and MLT of the footpoints of T01 model field lines mapped from POLAR. Otherwise, data is presented in the same format as Fig. 2.
The boundary plasma sheet (BPS) and central plasma sheet (CPS) are the regions where the discrete and diffuse aurorae are observed, respectively, as described by Winning-ham et al. (1975). The defining characteristic of CPS precip-itation is given to be high-energy plasma (several keV elec-trons and tens of keV ions) with comparatively little spatial
or spectral structure. The BPS lies poleward of the CPS and is characterised by slightly lower energies and intensities and more spatially and spectrally structured ion and electron spectra than observed in the CPS. However, the key to dis-tinguishing BPS from CPS precipitation is the fact that most discrete auroral arcs and acceleration events are embedded
Table 1. Typical average ion energies and integral fluxes used as part of the ionospheric precipitation classification (based on examples given in Newell et al. 1991b, c). Acronyms used: LLBL – Low-latitude Boundary Layer, BPS – Boundary Plasma Sheet, CPS – Central Plasma Sheet. These regions are described in Sect. 4.
Classification of Average Ion Energy/ Integral Energy Flux/ Particle Precipitation eV 108eV.cm−2.s−1
Void – 1.0–3.0 Polar Rain – 1.0–3.0 Mantle 300–1 000 1.0–100 Cusp 800–2000 300–1000 LLBL 3 000–5 000 100–500 BPS (Midnight/Dusk) 10 000–25 000 10–100 BPS (Noon/Dawn) 1000–10 000 2.0–300 CPS (Midnight/Dusk) 10 000–30 000 30–300 CPS (Noon/Dawn) 300–8000 1.0–50
within the lower energy background BPS electron precipita-tion. Feldstein and Galperin (1985) and Galperin and Feld-stein (1991) argue that the CPS maps to the near-Earth region of quasi-dipolar field lines; and the BPS to the distant plasma sheet and to the plasma sheet boundary layer (PSBL). How-ever, as all PSBL field lines cross the tail neutral sheet, the CPS/PSBL distinction is to some extent qualitative (Newell et al., 1991c). From this description, and the fact that ion energies are greater around dusk and midnight than dawn and noon (see Table 1), we would expect the CPS and BPS regions to relate to the dawn-dusk asymmetry discussed by Stubbs et al.
5 Results and interpretation
5.1 DCR peak ion energy occurrence distributions and comparison with Stubbs et al. He2+ion survey At the ion energies detectable by MICS in the cusp region we are observing the high-energy tail of the cusp ion distribu-tion. Under southward IMF conditions, the cusp particles are accelerated at the dayside magnetopause while crossing the rotational discontinuity (RD) resulting from subsolar recon-nection. Under northward IMF conditions, particles are also accelerated on crossing an RD, if the magnetosheath flow adjacent to the tail-lobe is sub-Alfv´enic such that reconnec-tion can occur. By analysing a time stareconnec-tionary RD in the de Hoffman-Teller (dHT) frame and then transforming back into the Earth’s frame we obtain the Wal´en relation
V = VH T ±VA (2)
(Hudson, 1970). In this equation V is the plasma velocity;
VH T is the speed of the dHT frame (in which the electric
field is zero) and can be thought of as the velocity of field line motion along the magnetopause; and VAis the local Alfv´en
speed (VA=B/(µ0ρ)1/2). The + and − apply on opposite
sides of the reconnection X-line and depend on the sense of the boundary-normal field. Depending on the orientation of
VH T with respect to B (and hence VA), plasma is either
accelerated or decelerated by VAon crossing an RD.
There-fore, the associated increase in particle energy is proportional to the particle mass, as all particles receive the same change in velocity on crossing the RD.
Clearly the relative increase in energy received by H+and He2+ions is dependent on their initial energies in the mag-netosheath and VA. In the depletion layer around the
subso-lar magnetosheath, proton temperatures are typically about 3.8×106K and plasma flow is of the order of 100 km.s−1 un-der high magnetic shear conditions (Phan et al., 1994). For low magnetic shear conditions, temperatures in the dataset presented by these authors were slightly lower and plasma flows were a little faster. VA at the dayside magnetopause
varies between around 100 and 300 km.s−1, but is typically about 200 km.s−1(Phan et al., 1996). Fuselier et al. (1991)
showed that in the depletion layer the ratio of He2+to H+
temperatures is typically ≈4.5. From these assumptions, we estimate that He2+ and H+ ions in the depletion layer have energies of around 2.6 keV and 0.6 keV, respectively. In the cusp, subsequent to being accelerated across the RD, we would expect He2+and H+ion energies of around 3.5 keV and 0.8 keV, respectively, a difference of about a factor of 4. For tail-lobe reconnection we would expect a similar differ-ence between He2+and H+ ion energies in the cusp. Al-though the initial temperatures in the magnetosheath would be lower and the acceleration at the RD would be signif-icantly less, the bulk flow in the magnetosheath, however, would be considerably faster.
For particles drifting in from the tail it is harder to predict their energies, as they have more complicated trajectories. The E×B drift acts towards the dawn flank and is depen-dent only on the ambient electric and magnetic fields. The gradient/curvature drift acts towards the dusk flank and de-pends on particle energy and charge. Using a crude analytical analysis we can estimate the energy at which these two com-peting drifts balance, referred to here as the cross-over en-ergy. If we consider the dipole field case, we can deter-mine the average velocities <vE>and <vB>for the E×B
0 10 20 30 40 50 60 70 80 90 −2 0 2 4 6 8 10 α / ° ∆ MLAT / °
Proton Energy = 1 keV
Field−aligned distance to DMSP = 16 RE
POLAR radial location in cusp = 7 RE
Ionospheric convection velocity, VC = 1 km.s−1
Fig. 4. The estimated difference in the MLAT of 1 keV H+ cusp ions observed at POLAR and DMSP (1MLAT) as a function of ion pitch angle (α). 1MLAT >0 indicates that cusp ions are observed further poleward at POLAR than at DMSP, and vice versa. Here we have assumed a field-aligned distance from the subsolar reconnec-tion X-line to DMSP and POLAR of ≈15 REand ≈9 RE, respec-tively; and an ionospheric convection velocity, VC=1 km.s−1.
and gradient/curvature drift motions, respectively, by inte-grating over the gyration and bounce motions. If the plasma distribution function is isotropic, then the energy at which
<vE>/<vB>=1, i.e. the cross-over energy, is given by
Kce ≈GQECL =2.3QECL (3)
in units of keV (see Appendix A for a derivation of this equation). In the above equation: Q is the charge state (dimensionless integer); EC is the convection electric field
(mV.m−1); L is the magnetic shell (dimensionless); G is a constant (keV.(mV.m−1)−1.RE−1). This equation tells us
that for the same ambient conditions, the cross-over energy is proportional to charge. In addition to this drift effect, He2+ ions are also accelerated to higher energies relative to H+ ions during each crossing of the mid-tail current sheet (On-sager and Mukai, 1995). (This is the same process that oc-curs at the magnetopause rotational discontinuity discussed above.) As a result, we expect a dawn-dusk asymmetry in the H+ions that flips at energies at least a factor of two less
than observed in the Stubbs et al. He2+ ion survey. Given that Kce≈23 keV for He2+ions, we would, therefore, expect
the cross-over energy to be below ≈10 keV for H+ions. Figure 2a shows that for peak ion energies from 0.9 to 1.1 keV, the occurrences are concentrated around noon, with a slight bias toward the pre-noon sector, and centred at
3≈81◦. This corresponds to the region previously identi-fied as the cusp in Figs. 6a and 6b of the Stubbs et al. We also note that the peak ion energies in the cusp (≈1 keV) are around a factor of four less than those observed in Stubbs et al. (≈4.3 keV), broadly consistent with higher He2+ tem-peratures in the depletion layer and the effects of
acceler-ation across a rotacceler-ational discontinuity at the magnetopause discussed above. Discrepancies between predicted and ob-served ion energies are likely due to the fact that a large por-tion of the cusp ion distribupor-tion is at energies below 1 keV, as well as the errors involved in this type of calculation for statistical observations based on typical values. This distri-bution extends further around the dawn flank, suggesting that we are also observing part of the LLBL identified in Fig. 1d of Newell and Meng (on either open or closed field lines). In-cluded in these occurrences are also intervals when POLAR traversed the magnetosheath, as discussed in the Stubbs et al. (2003) survey of extended cusp-like regions observed by CAMMICE MICS. In terms of the peak ion energy used in this study, these occurrences are impossible to distinguish from those on open field lines within the magnetosphere.
We also sorted the cusp occurrences shown in Fig. 2a by the sense of the IMF BZ component (not shown), which
showed that the cusp occurred at these energies under both northward and southward IMF conditions. The occurrences around noon for southward IMF conditions were higher than for northward IMF conditions, so we would expect the south-ward IMF cusp to be more dominant in Fig. 2a. As ex-pected, the southward IMF cusp was observed further equa-torward. The cusp had a pre-noon bias for both senses of IMF BZ, with the bias being strongest for northward IMF.
The southward IMF cusp was broader in 3 (≈6◦compared with ≈4.5◦) and narrower in MLT (≈3 h compared with
≈4 h). This is consistent with the arguments presented above. Figure 2b shows the occurrences for energies from 1.2 to 2.6 keV, which clearly isolate the asymmetric dawn feature centred around 3≈79◦, as previously shown in Stubbs et al.
(Figs. 6c and 6d). Due to the higher sampling rates afforded by the DCR channel, this asymmetry is more distinct than in the data from the He2+ion channel. From comparison with the LLBL and BPS occurrences shown in Figs. 1d and 1e, respectively, of Newell and Meng, the occurrences here appear to have contributions from the LLBL in the pre-noon sector and the BPS further dawnward around 06:00 MLT. To-gether with the pre-noon bias in the occurrences observed in Fig. 2a, it appears that a large component of the LLBL ob-served here in the pre-noon sector is on closed field lines and has been formed from low energy ions convecting earthward from the tail. Also, any LLBL ions in Fig. 2a appear closer to noon than those observed in Fig. 2b. This is consistent with drift motion theory (Lyons and Williams, 1984b), which pre-dicts that lower energy ions will drift around to the dayside as opposed to being scattered at the morning side of the mag-netopause. The formation of the LLBL, and whether or not it is on open or closed field lines, has important implications for the nature of the coupling between the solar wind and the magnetosphere (e.g. Lockwood, 1997).
For peak ion energies ranging from 2.9 to 8.0 keV the oc-currences are roughly symmetric about the noon-midnight meridian, as shown by Fig. 2c. This suggests that we have isolated the range of energies where the opposing E×B and gradient/curvature drifts balance: the crossover energy. This appears to correspond to a transition between the ions
observed in Stubbs et al. (Figs. 6c and 6d, Figs. 6e and 6f). We also notice that the occurrences are more poleward on the dusk flank (centred about 3≈77◦) than on the dawn flank
(centred about 3≈75◦); this looks similar to the BPS distri-bution presented in Fig. 1e of Newell and Meng. This differ-ence in the 3 of peak occurrdiffer-ence on the dawn and dusk flanks indicates that the drift orbits take ions closer to the Earth on the dawn flank at these energies, and appears to be consistent with the drift orbits shown in Lyons and Williams (1984b) at the transition between dawn and dusk dominated flow.
At the higher energies ranging from 9.1 to 25.2 keV the asymmetry has made the change from the dawn to the dusk flank, with the highest occurrences around the noon and post-noon sectors, as shown in Fig. 2d. This appears to relate to the distributions shown in Figs. 6e and 6f of Stubbs et al., where we also observe occurrences ranging from 3≈66◦to
76◦and extending over a large range of local times. This is again consistent with ion drift trajectories predicted at these energies where ions drift around to the dayside from dusk and scatter at the magnetopause before reaching the dawn flank (Lyons and Williams, 1984b). These occurrence probabili-ties appear to relate in part to the CPS population identified in Fig. 1f of Newell and Meng.
From the observations in Figs. 2c and 2d the cross-over energy appears to be at about ≈9 keV. As predicted, this is over a factor of two less than the cross-over energy observed for He2+ions by Stubbs et al. (Kce≈23 keV). Therefore, this
result is consistent with drift orbits and ion acceleration in the mid-tail current sheet, as discussed earlier.
5.2 DCR average ion energy occurrence distributions and comparison with Newell and Meng DMSP survey In this section, we concentrate on comparing the distribution of the DCR average ion energy occurrence probabilities with the study by Newell and Meng. Figure 3a shows the DCR average ion energies from 0.9 to 1.53 keV. In this figure we can identify the cusp around noon, centred at MLAT ≈80.5◦ and ≈11:45 MLT, with an MLT extent of ≈3 h noticeably biased toward the pre-noon sector. The occurrence of cusp in Newell and Meng’s survey, as shown in their Fig. 1b, is confined – extending only 2.5 h in MLT and centred at MLAT
≈78.5◦and ≈11:45 MLT. Both extend for ≈5◦in MLAT. The discrepancy in cusp latitudes of around 2◦in MLAT between observations made at POLAR and DMSP is con-sistent with the result of convection effects. The precipi-tating ions observed at low altitudes by DMSP are highly field-aligned when they leave the magnetopause: pitch an-gles increase up to near 90◦only close to the satellite, where the field strength is very high. The instruments on DMSP satellites do not resolve pitch angle and in the cusp region, where elapsed times since reconnection are relatively small, observed fluxes are dominated by ions that have the short-est time-of-flight from the reconnection site to the iono-sphere, i.e. field-aligned ions. (This is especially true at energies above 1 keV, as used in the survey presented here.) At POLAR altitudes, MICS observes a much broader range
of pitch angles and as a result the time-of-flight of the ions varies considerably for any given energy observed. In the cusp, MICS tends to observe ion pitch angle distributions peaking around the field-perpendicular directions at pitch angles of 90◦ and 270◦, as well as often missing the field-aligned and anti-field-field-aligned populations (at pitch angles of 0◦ and 180◦, respectively); this is due to the magnetic field direction moving out of the plane observed by the instrument, which is perpendicular to the satellite spin axis (e.g. Stubbs et al., 2000).
Figure 4 shows the estimated differences in MLAT as a function of ion pitch angle (α) expected for 1 keV cusp ions. Here we have assumed a typical field-aligned distance of
≈15 REfrom the reconnection X-line to the ionosphere; and
that POLAR is typically at a radial distance of ≈7 RE when
observing the cusp (i.e. we assume a ≈9 RE field-aligned
distance from POLAR to the X-line). The T01 model is used to determine the field-aligned distances used to com-pute the ion flight times. We also assume that the footpoint of the field line is convecting through the ionosphere at a typ-ical velocity, VC=1 km.s−1, which is roughly 8×10−3◦ (in
MLAT).s−1. For α<50◦, we can see that cusp ions are pre-dicted to be observed further equatorward at POLAR than at DMSP, due to the shorter field-aligned distance to the X-line. However, once α>50◦, cusp ions are expected to be observed further poleward at POLAR than at DMSP, and 1MLAT in-creases rapidly with α. Given the differences in the ion pitch angle distributions observed at POLAR and DMSP, as dis-cussed above, these convection effects can explain the ob-served ≈2◦difference in MLAT. Also, in the MICS observa-tions there will be a contribution from upgoing ions that have mirrored at low altitudes in the cusp and are travelling in the anti-field-aligned direction away from the Earth; this would again be expected to shift the cusp observations at POLAR further poleward of those at DMSP, as observed.
In Fig. 3a, it is unlikely that there is a significant contribu-tion from the mantle populacontribu-tion shown in Fig. 1c of Newell and Meng, as that has a broad range in local time, unlike the occurrences shown here. Mantle ions are expected to have lower energies than cusp ions, so the majority probably fall below the energy threshold of MICS.
The distribution of average ion energies from 1.53 to 2.10 keV is shown in Fig. 3b. The peak in the occur-rence of ions at these energies is distributed between MLAT
≈76.5◦and ≈81.5◦and extends for about 8 h in MLT centred about 09:00 MLT. This appears to relate to the LLBL identi-fied in Fig. 1d of Newell and Meng, which peaks between MLAT ≈76◦ and ≈80◦ and extends for about 6 h centred
around 10:30 MLT. Time-of-flight arguments demand that equatorward of the cusp precipitation must lie on open LLBL (Lockwood and Smith, 1993; Lockwood, 1997). The strong pre-noon bias of these occurrences appears to also relate to the dawn asymmetry in Fig. 2b, again strongly suggesting that the majority of LLBL ions away from noon are on closed field lines and have drifted earthward from the tail. This drift can continue onto open field lines but only while the particles coming from closed field lines precipitate, mirror and return
to the spacecraft (i.e. up to half a particle bounce period): only after this time will the effect of the lack of supply of trapped particles be seen by the spacecraft. Thus, the ions can only penetrate by drifts onto the low-latitude edge of the open polar cap. The peak in the occurrence of this LLBL ion population originating on closed field lines appears to be about 1◦ in MLAT further poleward when observed at POLAR than when observed at DMSP. This discrepancy in MLAT could be due to the fact that the closed LLBL ions observed at DMSP have been scattered into the loss cone, whereas POLAR observes the bulk of the population on drift orbits. However, it could also reflect poleward drift, as in the case of the cusp ions discussed above, if magnetopause re-connection extends to the pre-noon sector. POLAR observes higher occurrences at around 06:00 MLT than DMSP; this is caused by low energy BPS ions which are part of the over-all BPS population identified in Fig. 1e of Newell and Meng. The identification of these ions as BPS by Newell and Meng is likely due to their more sophisticated classification meth-ods.
The open LLBL near noon observed at POLAR centred about MLAT ≈78.5◦ appears to be about 0.5◦ in MLAT further poleward of that observed by DMSP centred about MLAT ≈78◦. This is a result of the convection effects used to explain the discrepancy in cusp locations discussed above. The discrepancy here is less than in the cusp (1MLAT ≈0.5◦ for the LLBL, as opposed to 1MLAT≈2◦for the cusp) due to the higher LLBL ion energies and the more field-aligned nature of LLBL population typically observed at POLAR. In both the POLAR and DMSP observations the open LLBL is equatorward of the cusp and is thus consistent with the energy-dispersed ion signatures expected to result from sub-solar reconnection.
We sorted the occurrences in Figs. 3a and 3b by the sense of the IMF BZ component (not shown) and showed that for
both senses the cusp occurred poleward of the LLBL. These features were observed further poleward for northward IMF conditions. This is consistent with the effects of magne-topause reconnection for cusp ions, and LLBL ions drifting earthward from the tail on closed field lines (a weaker EC
un-der IMF BZ>0 causes ion drift orbits further from the Earth,
which then map to higher latitudes).
Figures 3a and 3b both have small, but significant, occur-rence probabilities in the region about MLAT ≈90◦. This possibly relates to polar rain, as described by Newell and Meng, though it is more likely polar wind created by up-welling ionospheric plasma (e.g. Lockwood et al., 1985).
Figure 3c shows the distribution for average ion energies ranging from 2.10 to 4.85 keV. In this distribution the peak occurrences range from MLAT ≈70◦ to 79◦ on the dawn flank and from MLAT ≈70◦to 81◦on the dusk flank. This is consistent with the BPS shown in Fig. 1e of Newell and Meng and the occurrences in Fig. 2c, both of which extend to higher latitudes at dusk. The similarity with occurrences in Fig. 2c, where the distribution is roughly symmetric about the noon-midnight meridian, indicates that the E×B and gradient/curvature drifts are balancing at these energies.
Figure 3c shows a clear gap around noon in the BPS popu-lation, consistent with these particles convecting sunward on closed field lines. However, there are a significant number of cases in which >2 keV ions are seen within this gap. From their MLAT and MLT, these lie immediately equatorward of the open LLBL and cusp particles near noon and thus are likely to be open BPS particles as proposed by Lockwood (1997). These could have resulted from acceleration of mag-netospheric particles at the interior RD launched by the re-connection site (standing in the inflow to the magnetopause on the magnetospheric side of the boundary, whereas the main magnetopause current sheet is the corresponding RD standing in the inflow on the magnetosheath side), as mod-elled by Lockwood et al. (1996). Alternatively, these may have resulted from acceleration at the bow shock, as pro-posed by Fuselier et al. (1999). Such “open BPS” is likely to have very narrow latitudinal width and so could have been missed in this survey with 1.5◦MLAT bin widths. However,
occurrences were only slightly increased in the survey that used 0.5◦MLAT bin width. We conclude that some BPS particles can be found on open field lines, but they are rare – possibly because the interior RD and/or the Fermi accel-eration mechanisms only rarely elevate ions to BPS energies and most such particles are found in the open LLBL.
Figure 3d shows the distribution for energies ranging from 4.85 to 8.55 keV. The peaks in the occurrences are centred about MLAT ≈70◦on both flanks, and cover a broader range of latitudes on the dawn flank than on the dusk flank. By comparison with occurrences in Figs. 1e and 1f of Newell and Meng, the dawn flank occurrences relate to the CPS and the dusk flank occurrences relate to the BPS, respectively. We also notice the appearance of occurrences below MLAT
≈67◦in Figs. 3c and d, particularly on the dawn flank.
Figures 3e and f show the distribution of ions with energies from 8.55 to 15.20 keV and 15.20 to 26.83 keV, respectively. The narrow band of occurrences on the dawn flank centred about MLAT ≈65◦ in Fig. 3e is consistent with the CPS shown in Fig. 1f of Newell and Meng. However, the peak in the occurrences are beginning to slip below MLAT ≈67◦(at these latitudes MLAT ≈3, so L≈6.6), which means that ring current ions are beginning to contribute to the background occurrences. These ions are trapped on closed field lines and have not immediately drifted earthward from the tail. We also note that these occurrences tend toward the dusk flank, showing a change in asymmetry at these latitudes compared with the occurrences shown in Figs. 3c and 3d. Again, this fits with the drift orbit hypothesis for ions at these energies drifting around to the dayside magnetopause from the dusk flank and scattering at the magnetopause before reaching the dawn flank (Lyons and Williams, 1984b). The portion of the distribution in Figs. 3c and 3f below MLAT ≈65◦at dawn and MLAT ≈70◦at dusk appears to relate to the region de-scribed by Newell and Meng as void where there is negligible ion precipitation into the ionosphere.
Within the BPS/CPS precipitation regions there is the tran-sition from E×B to gradient/curvature drift dominated flow. This transition is expected to be a gradual process from keV
to tens of keV energies, as ion trajectories evolve from flow-ing mostly towards dawn to flowflow-ing mostly toward dusk (see Figs. 4.25 and 4.27 of Lyons and Williams, 1984b). The nar-row band of high occurrences in Fig. 3e marks the full tran-sition to gradient/curvature drift dominated ion trajectories. This qualitatively explains the distribution of ions precipitat-ing into the auroral oval.
6 Discussion and conclusions
The surveys presented in this paper enable us to relate the studies of Stubbs et al. and Newell and Meng in terms of both ion energy and location in latitude and MLT. We are able to qualitatively explain the lower DCR cusp energies relative to the He2+ion survey by magnetic reconnection re-lated acceleration processes at the magnetopause. We show that the similar decrease in the magnitude of the cross-over energy for particles on drift orbits can be explained in terms of the competing E×B and gradient/curvature drifts, and acceleration by Alfv´en waves as ions cross the tail current sheet (Onsager and Mukai, 1995). The ion observations here also support the observations and interpretations of Friedel et al. (2001), based mainly on electron data, that plasma trans-port can be well explained by drift orbit theory.
Open field line features are observed at energies around
≈1 keV in the DCR channel and distributed about noon with a slight pre-noon bias. As expected, ion occurrences are ob-served at lower latitudes in Fig. 3 than in Fig. 2 due to the dif-ferences between 3 and MLAT discussed in Sect. 2. There are also slight differences between the energies observed in Figs. 2 and 3, due to the differences in determining the peak in the JE spectra and calculating the average ion energy, as
detailed in Sect. 3.
Cusp and open LLBL ions observed at POLAR, as shown in Figs. 3a and b, respectively, are around ≈1◦to 2◦higher in MLAT than those observed by Newell and Meng. How-ever, these differences are shown to be consistent with the differences expected due to energy and pitch-angle depen-dent dispersion caused by convection during the time-of-flight from the reconnection X-line to POLAR or DMSP. These effects mean that the slower an ion’s field-aligned ve-locity, the longer it remains on a field line; thus allowing it to reach higher latitudes the further it convects in the anti-sunward direction. The DMSP SSJ/4 instruments only ob-serve near field-aligned ions (which have the shortest time-of-flight from the reconnection X-line) compared with MICS aboard POLAR, which observes ions with a range of pitch angles that have relatively longer time-of-flights. Hence, even though POLAR was closer to the X-line, it observes ions at higher latitudes than DMSP, as the field-aligned ve-locities of the ions observed by MICS were less than those observed by DMSP for any given energy. In Fig. 4 we show that we expect the cusp to be observed further poleward by POLAR for ions with pitch angles greater than ≈50◦. The poleward location of the cusp at POLAR could also be in part due to ions that have mirrored at low altitudes and are
travelling away from the Earth. We also note that the open LLBL around noon is, on average, equatorward of the cusp, so this is consistent with the energy-dispersed signature ex-pected for subsolar reconnection.
We also present evidence in Figs. 2b and 3b that the pre-noon bias in the occurrence of LLBL particles observed by Newell and Meng is most likely caused by the component of the LLBL coming from closed field lines formed by low en-ergy ions drifting earthward from the tail; and thus relates in part to the dawn-dusk asymmetry observed by Stubbs et al. in He2+ion occurrences. These ions mainly remain on closed field lines but the drift can continue onto open field lines for up to half a particle bounce period. We also note that the oc-currences around 06:00 MLT in Fig. 3b have a contribution from the lower energy component of the BPS ion population, as identified in Fig. 1e of Newell and Meng. The implica-tions for the formation of the LLBL and momentum transfer are important. There is an open LLBL immediately equator-ward of the cusp caused by reconnection and there appears to be an LLBL on the dawn flank only, consistent with particles drifting sunward. These ions can penetrate onto open field lines but only in a thin latitudinal band and will primarily be on closed field lines. Thus, the sheath plasma on the open LLBL field lines is consistent with entry along open field lines that subsequently close in the tail and convect sunward. We conclude that the closed LLBL does not provide evidence for transfer of mass and momentum from the solar wind to the LLBL by some non-reconnection (“viscous-like”) inter-action, but that these ions were originally injected onto open field lines which were subsequently closed by tail reconnec-tion. The observed LLBL ions then migrated sunward from the tail, preferentially to the dawn flank because their energy was below the “cross-over energy”.
At higher energies (≈2 to 20 keV), the distribution tends towards the region of the auroral oval. This relates to the BPS and CPS populations, where ions make the transition from dawnward to duskward dominated flow with increas-ing energy to form the dawn-dusk asymmetry. In particular, the ion population at the cross-over energy seems to relate to the BPS in terms of both energy and location in latitude and MLT. Table 1 shows that both the BPS and CPS ions have higher energies at dusk than at dawn. This leads to the oc-currences from the dawn BPS appearing in Figs. 3b and c and the dusk BPS appearing in Figs. 3c and d. This is similarly shown for the CPS in Figs. 3d and e. These overlaps in the average energy and location of the plasma populations clas-sified by Newell and Meng are to be expected, as they used a more sophisticated set of selection criteria.
We have related statistical observations made at different altitudes in the magnetosphere-ionosphere system and shown them to be consistent. We have explained the observed oc-currence distributions in terms of ion injection at the dayside magnetopause and the transport of ions earthward from the tail along drift orbit trajectories. We have also produced ev-idence that the component of the LLBL on closed field lines has drifted earthward from the tail and, therefore, has not entered directly from the dayside magnetopause. This has
important consequences for how we understand the coupling between the solar wind and magnetosphere. Ions at ener-gies around the cross-over energy relate to the BPS and CPS populations, and are thus important in understanding the in-fluence of drift orbits on the location and behaviour of ions in the auroral oval. To fully test the qualitative explanations given here for these observations will require a comparison with numerical simulations; this will hopefully be the subject of a future paper.
Appendix A
Deriving the estimate for the cross-over energy
We calculate a crude estimate for the cross-over energy to establish if the flip in asymmetry about the noon-midnight meridian can be explained by drift orbits. This estimate is only expected to be approximately accurate, as we need to make simplifying assumptions to obtain an analytical solu-tion. The drifts due to the electric field (E) and the gradient (∇B) and curvature (RC) of the magnetic field are given by
Eqs. (A1), (A2) and (A3), respectively.
VE = E × B B2 (A1) V∇ = mν⊥2 2qB3(B × ∇B) (A2) VR= mνk2 q Rc×B RC2B2 (A3)
In the above equations: v⊥and vkare the perpendicular and
parallel velocity components relative to the magnetic field (B); m and q are particle mass and charge, respectively. If we assume that currents are negligible, we can combine the gradient and curvature drifts, vRand v∇, respectively, to
ob-tain the total magnetic drift,
VB =VR+V∇= v2k+1 2ν 2 ⊥ B × ∇B ωgB2 = W qB3(1 + cos 2α)B × ∇B; (A4)
where ωg is the particle gyro-frequency (Lyons and
Williams, 1984a; Baumjohann and Treumann, 1997). In re-ality, a particle in a dipole field will gyrate, bounce and drift all at the same time. To determine the slower drift motion we must integrate over the gyration and bounce motions. The average total magnetic drift is given by
< νB>≈
6W
qBeqreq
(0.35 + 0.15 sin αeq), (A5)
where req is the equatorial crossing distance from the centre
of the Earth, and Beq is the magnetic field magnitude in the
equatorial plane (See Lyons and Williams (1984a) or Stubbs (2002) for a more rigorous derivation).
As can be seen from Eq. (A5), <vB> has only a weak
dependence on equatorial pitch angle. There is a stronger dependence on particle charge, energy and magnetic field geometry, but no dependence on particle mass (Lyons and Williams, 1984a). We would thus expect different ion species with the same energy and charge state to drift with the same magnetic drift velocity, e.g. H+and He+ions.
The solar wind generates an electric field inside the mag-netosphere, E=−Vsw×B, which is able to penetrate via
open magnetic flux, particularly during periods of southward IMF. This electric field is referred to as the convection elec-tric field, EC, and is directed from dawn to dusk in the
equa-torial plane, so particles will experience an E×B drift, as described by Eq. (A1).
We can obtain an average value for the electric field drift velocity,
< νE>≈
E⊥eq
Beq
(A6)
(Lyons and Williams, 1984a; Stubbs, 2002). Here E⊥eq is
the electric field perpendicular to the Sun-Earth line in the equatorial plane.
We can write Eq. (A5) for the average total magnetic drift velocity and Eq. (A6) for the average electric drift velocity as a function of the magnetic shell, L (assumed to be equivalent to the McIlwain L-shell) to give
< νB>≈ 6W L2 qBERE (0.35 + 0.15 sin αeq) (A7) and < νE>≈ E⊥eqL3 BE . (A8)
In these equations, BEis the equatorial magnetic field
mag-nitude at the surface of the Earth, RE is the radius of the
Earth, and αeq is the particle pitch angle in the equatorial
plane. (Here we have also used the equations: req=LREand
Beq=BE/L3.)
If we assume that the cross-over energy, Kce, occurs when
the drift velocities are equal and opposite, then from Eq. (A7) and (A8) we obtain
Kce=
qE⊥eqLRE
6(0.35 + 0.15 sin αeq)
. (A9)
Given the assumption that the pitch angle distribution at the equator is isotropic, we can substitute αI for αeq, where
sin αI= r 2 3
, given that ν⊥2=2ν2k for an isotropic distribu-tion. We also assume that the dominant electric field in the near-Earth tail is the convection electric field, EC. Using
these substitutions we obtain
Kce≈GQECL =2.3QECL. (A10)
Here Kce is the cross-over energy (keV); Q is the charge
field (mV.m−1); L is the L-shell (magnetic shell,
dimension-less); G is a constant (keV.(mV.m−1)−1.R−1
E ).
We assume that an isotropic equatorial ion pitch angle is reasonable as Kce does not have a strong αeq dependence.
This can be demonstrated by calculating G for an αeq of 10◦
and 90◦, which gives values of ≈2.8 and ≈2.1, respectively. Acknowledgements. This work was funded by PPARC. T. J. Stubbs was also funded by the National Research Council whilst working at NASA/GSFC. We thank the many individuals who have made the CAMMICE program (PI T. A. Fritz) a success. We are grateful to P. T. Newell for useful discussions on how best to compare our results with his DMSP study. Thanks to S. J. Schwartz for discus-sions about ions in the magnetosheath. Thanks also to J. Scuffham for assistance with the T01 model. We benefited from use of WIND MFI and SWE data (PIs R. P. Lepping and K. W. Ogilvie, respec-tively) obtained from CDAWeb and Dst data obtained from NSSDC OMNIWeb, both of which are managed by SPDF at NASA/GSFC. Figure 1 was reproduced and modified by permission of the Amer-ican Geophysical Union.
Topical Editor T. Pulkkinen thanks two referees for their help in evaluating this paper.
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